What type of limestone is found in caves?

The type or more accurately, age and lithology, of the limestone does not influence cave development within it significantly, though its structure will.

CALCITE, the mineral Calcium Carbonate, is deposited in caves as Stalactites, Stalagmites and related formations, having been dissolved from the limestone above.

The original answer said Travertine, but although that is the same mineral, it is a form deposited in the open air.